Robust MIMO Equalization for Non-Parametric Channel Model Uncertainty

In this paper, three MIMO robust equalization problems are considered for non-parametric classes of channel models defined by weighted H2 or H∞ balls (of frequency-responses) and performance criteria based on H2 (variance) or H∞ norms of error signals. The approach pursued here centers on characterizing the worst-case performance of candidate equalizers, or upper bounds on it, by means of dual Lagrangian functionals. Then, for linearly parametrized, finite-dimensional classes of candidate equalizers, the corresponding robust equalization problems are converted into semi-definite linear programming problems for which approximate solutions can be effectively computed. A simple numerical example is presented, involving H₂ model uncertainty and error-variance performance, to illustrate, for various levels of uncertainty, the changes in the worst-case performances of the nominally optimal equalizer and of the one, in a specific linear class, which minimizes the worst-case error variance.